Phase Transition Front Research Articles

Modeling triangular titration fronts in the O2+H2 reaction on a catalytic Rh(111) surface

We present a model for the titration of an oxygen saturated catalytic Rh(111) surface with hydrogen. Oxygen is removed by reaction-diffusion fronts. Experimentally, these fronts have been observed to be either isotropic or triangular depending on the conditions of preparation of the oxygen layer as well as on temperature and hydrogen pressure. If we model only the surface reaction and the diffusion of hydrogen, we obtain isotropic fronts with velocities in the range of 2–3 μm s−1. These results are in line with experimental measurements for surfaces exposed to oxygen for a short period. To correctly reproduce the possible triangular shape of the titration fronts and the smaller front velocities of 0.1–1 μm s−1 for experiments with the surface exposed to oxygen for a long time (>1 h), we have to include the formation of a subsurface oxygen-rich phase and its removal. It is assumed that the phase transition between the oxygen-rich and oxygen-free subsurface phases occurs via front propagation, and the front speed has triangular symmetry compatible with the symmetry of the crystalline bulk. By fitting parameters describing the propagation of the phase transition front, its anisotropy and its coupling to the reaction-diffusion front on the surface, we have been able to quantitatively reproduce all experimental observations presented by Schaak and Imbihl in Chem. Phys. Lett. 283, 386 (1998).

THERMOELASTIC WAVE AND FRONT PROPAGATION

The propagation of thermoelastic waves and phase-transition fronts is considered in a unified manner on the basis of thermodynamic consistency conditions following from the thermodynamics of discrete systems. Distinct consistency conditions are used in the bulk (for thermoelastic waves) and at the phase boundary (where entropy is produced). It is shown that the thermodynamic consistency conditions in the bulk lead to the well-established numerical schemes. Examples of the propagation of two-dimensional thermoelastic waves in media with rapidly varying properties (e.g., in functionally graded materials) are presented. The criterion of initiation of the phase transformation process is obtained by simultaneously satisfying both consistency conditions at the phase boundary. The comparison with the experimental investigations of the impact-induced martensitic phase transformation is also given.

"Material" mechanics of materials

The paper outlines recent developments and prospects in the application of the continuum mechanics expressed intrinsically on the material manifold itself. This includes applications to materially inhomogeneous materials physical effects which, in this vision, manifest themselves as quasi-in homogeneities, and the notion of thermo dynamical driving force of the dissipative progress of singular point sets on the material manifold with special emphasis on fracture, shock waves and phase-transition fronts. .

Feeding and dissipative waves in fracture and phase transition: II. Phase-transition waves

Discrete and homogeneous models of a structured material are considered to resolve difficulties in the analysis of dynamic phase transition. The discrete model is a chain consisting of particles connected by massless bonds, while the continuous model is represented by a partial differential equation with higher than the second order of coordinate derivatives. The macrolevel constitutive law is represented by a bi-linear stress–strain relation, such that the transition from the first, stiffer phase to the second one is irreversible. Solutions of two types, macrolevel-associated and microlevel, are derived. The first type of solution is characterized by a macrolevel feeding wave (the wave delivering energy to the phase-transition front is of a zero wave number), while the microlevel solutions correspond to a nonzero feeding wave number. Subsonic, intersonic and supersonic phase-transition waves are described. For the homogeneous model it is shown that the contradiction between the limiting stress and energy criteria, inherent for the macrolevel formulation of the problem, is eliminated if and only if the phase transition does not concern the highest-order modulus. Total structure- and speed-dependent dissipation, as the energy carried by microlevel waves away from the phase-transition front, as well as parameters of each dissipative wave are determined. For the fourth-order partial differential equation, the existence of the Maxwell type, dissipation-free, subsonic phase-transition wave is shown. In this case, the microstructure plays the role of a catalyst. Common and distinctive properties of the discrete and homogeneous models are discussed.

Effect of radiation scattering on the melting and solidification of a flat layer of a translucent medium

The paper considers the effect of isotropic and anisotropic scattering of radiation on the melting (solidification) of a flat layer of a semitransparent medium between opaque surfaces. The mathematical model of the phase transition is the classical formulation of the Stefan problem. From results of numerical calculations it follows that radiation scattering has a significant effect on the rate of propagation of the phase transition front and formation of a temperature profile during melting (solidification) of a semitransparent medium.

Multi–Front Phase Transitions During Nonisothermal Filtration of Live Paraffin–Base Crude

By numerical modeling of nonisothermal filtration of multicomponent oil with allowance for the Joule—Thomson effect, adiabatic effect, and heat of phase transitions that occur during oil degassing and paraffin crystallization, the formation of profiles of phase–saturation, concentrations of oil components, and temperature in oil beds is studied. It is shown that consideration of many components results in occurrence of phase–transition fronts during degassing of oil components and paraffin crystallization. In turn, paraffin crystallization gives rise to temperature oscillations. Depending on the initial paraffin concentration and on the ratio of phase–transition heats for oil degassing and paraffin crystallization in an oil bed, either decaying or steady–state temperature oscillations are observed.

Regimes of Dissociation of Gas Hydrates Coexisting with a Gas in Natural Strata

A mathematical model of decomposition of gas hydrates that coexist with a gas in natural strata is proposed; the model takes into account the mobility of the liquid phase. Conditions at the unknown boundary of dissociation are derived. In the self-similar approximation, the solution is represented in the form of probability integrals. The obtained system of transcendental equations at the moving boundary has been investigated numerically in a wide range of parameters. It is shown that different regimes of dissociation in collectors with a positive initial temperature exist; these regimes correspond to the decomposition of a hydrate into gas and water and gas and ice and have both a sharp phase-transition front and are accompanied by the formation of an extended region of dissociation. On the plane of the main parameters of the process, the critical diagram is constructed and the existence domains of the solution of each form are singled out.

Low-temperature confinement of SIC-superthin film and superfine particles

Studies on phase transition of a model ionic conductor thin film sandwiched with insulators are theoretically carried out in terms of the interacting lattice gas model, and become a possibility if a low-temperature confinement of superionic conductors is realized. Due to a number of defects existing in the interface region, the defect-induced phase transition is promoted, giving rise to the order-disorder phase transition front. This suggests that a sandwiched superionic conductor thin film or superionic fine particles can be realized well below the bulk superionic transition temperature.

Nonsteady condensation and evaporation waves

We study the motion of a phase transition (PT) front at a constant temperature between stable and metastable states in fluids with the van der Waals equation of state. We focus on a case of relatively large metastability and low viscosity, when no steadily moving PT front exists. Simulating the one-dimensional hydrodynamic equations, we find that the PT front generates acoustic shocks in forward and backward directions. Through this mechanism, the nonsteady PT front drops its velocity and eventually stops. The shock wave may shuttle between the PT front and the system's edge, rarefaction waves appearing in the shuttle process. If the viscosity is below a certain threshold, a turbulent state sets in.

THERMOMECHANICS OF HETEROGENEOUS MATERIALS WITH WEAKLY NONLOCAL MICROSTRUCTURE

A unified thermomechanical framework is presented for the theory of mechanically elastic materials the physical description of which requires the consideration of additional variables of state and of their gradients (weak nonlocality). This includes both the case of additional degrees of freedom carrying their own inertia and the case of diffusiw internal variables of state. In view of practical applications to fracture and propagation of phasetransition fronts. special attention is paid to the construction and immediate consequences of the equations of balance of canonical momentum (on the material manifold) and energy at regular points and at jump discontinuities. In particular. the general expression of the dissipation at, and of the driving force acting on. phase-transition fronts is formally obtained in such a broad framework. Brief applications include thermoelastic conductors (e.g. shape-memory alloys) and elastic ferromagnets in which both spin inertia and ferromagnetic exchange forces (magnetic ordering) are taken into account.

Two-front mathematical model of water injection into a steam-saturated geothermal reservoir

A mathematical model of the process of water injection into a high-temperature steam-saturated geothermal reservoir is proposed. In the reservoir there is a zone of co-existence of steam and water which is separated from the steam and water zones by moving interfaces (phase transition fronts) whose location is determined in the process of solving the problem. Within the framework of the proposed model the thermodynamic contradiction that exists in the single-front case for low permeabilities, expressed as supercooling of the steam in the corresponding zone ahead of the interface [1, 2], is not observed. With increase in the permeability the two-front solution obtained goes smoothly over into a noncontradictory single-front solution. Neutral curves separating the domains of existence of the different types of solution in parameter space are constructed.

On the universality of the thermomechanics of forces driving singular sets

It is shown that the formal expression of the driving force acting on a one- dimensional or two-dimensional singular set of material points (crack tip in fracture, phase-transition front or shock wave) and of the accompanying dissipation in an irreversible progress of the set is independent of the precise material behaviour at regular points. A four-dimensional space-time canonical formalism is introduced establishing the necessary consistency between the power expended by the driving force (spatial component) and the resulting heat source (timelike component) localized at the singular set. Possible extensions of this result are discussed.

Thermal trapping and kinetics of martensitic phase boundaries

In this paper we study the influence of latent heat on kinetics of martensitic phase transitions and derive a relation between the velocity of an adiabatic phase boundary and the corresponding driving force (kinetic relation). Inside the phase transition front we adopt a non-isothermal version of the viscosity-capillarity model. We show that if the latent heat is different from zero, a finite value of the driving force must be reached, before the transition front can move; this effect of thermal trapping may contribute to martensitic hysteresis. In the adiabatic case the kinetic relations are non-monotone and non-single-valued, reproducing some fine features of the kinetic relations obtained previously for purely mechanical discrete models with bi-stable elements. We show that in its gross features, our kinetic model is similar to the conventional model of dry friction.

The role of canonical balance laws in the study of the progress of "defects" in microstructured materials

A unified thermomechanical framework is presented for deformable materials endowed with a weakly non-local microstructure. In view of practical applications to fracture and the progress of discontinuity fronts (shock waves, phase-transition fronts) special attention is paid to the construction and immediate consequences of the canonical equations of balance of momentum and of energy at regular points and singular sets. This leads to obtaining the expression of driving forces and of the associated dissipation, if any. The recently formalized theory of inhomogeneity and configurational forces on the material manifold (so-called Eshelby mechanics) is the appropriate setting for this as: (i) it pertains to the loss of translational symmetry on the material manifold, (ii) it automatically captures all fields simultaneously, and (iii) it emphasizes gradient effects, here a most appropriate feature.

Defect-Induced Surface Sublattice Melting of Ionic Conductor Thin Film –Parallel Ionic Conductivity–

Theoretical study on the ion-hopping conduction of an ionic conductor thin film sandwiched with insulators is carried out in terms of the interacting lattice gas model. The defect-induced phase transition is promoted due to plenty of defects existing in the interface region, giving rise to the maximum ionic conductivity near there, where it is the front of the order-disorder phase transition. This phase transition suggests that a sandwiched superionic conductor thin film can be realized at temperature far below the bulk superionic transition temperature.

On shock waves and phase-transition fronts in continua

The canonical formalism that considers simultaneously the second law of thermodynamics and the balance of canonical momentum is used to incorporate the case of shock waves among those singularity sets whose dissipation is in fact related to the power expanded by a driving force — a force on the material manifold and not in physical space — in an irreversible motion of the singularity set. A relationship between this and the presence of a generally non-zero quasi-inhomogeneity material force at the wave front is established. Extensions to electromagnetic continua of various types are given and the case of shock waves is thoroughly compared to that of phase-transition fronts in the same continua. The relationship with solitonic and moving localized dissipative structures is enunciated.

Decomposition of gas hydrates in low-temperature reservoirs

The process of dissociation of gas hydrates coexisting with gas and ice in low-temperature reservoirs is considered. A qualitative analysis of the phase transitions which enables possible configurations of the solutions to be predicted is carried out on the basis of the phase diagram for methane hydrate. Mathematical models of hydrate decomposition in reservoirs which take into account the formation of an extended dissociation zone and the presence of two phase transition fronts are proposed.

Competition between Relaxation Kinetics and Heat Transfer in the Dynamics of Phase Transition Fronts

The velocity of the interphase boundary motion caused by latent heat transfer at ferroelectric phase transitions is calculated. The criterion for separating of two mechanisms for the front motion - the latent heat transfer and the relaxation of the order parameter - is obtained for ferroelectrics. Electric field dynamics of interphase boundaries have been studied. The expression for the front velocity of the threshold field type is derived. The transition from a metastable phase to a thermodynamically stable phase takes place via fluctuations leading to the formation of nuclei of the new phase (heterophase fluctuations) (I). In order to describe systems which undergo a symmetry-breaking first-order phase transition, the nucleation and growth processes must be accounted for. The growth is associated with the propagation of interphase boundaries separating the high-temperature parent phase and the low-temperature product phase. In solid diffusiohless transformations the growth may be slow enough for the observation by polarization microscope technique. In particular, in ferroelectrics sharp interphase boundaries can be observed (2-121. Crystals with sharp interfaces most often have kinetically controlled rather than diffusion-limited growth. Usually the interphase dynamics are governed entirely by the time evolution of the order parameter (13-201, and the temperature can be considered to be a constant. Thus the heat is assumed to be removed rapidly enough that no temperature change occurs as the latent heat of the phase transition appears at the interphase boundary. However as the interface moves it acts as a heat source with a strength proportional to the latent heat and the forward rate of motion, giving rise to a jump in the thermal gradient. The heat generated during the interphase boundary motion can accelerate the interface which, in turn, increases the heat production rate. A system involved in this avalanche-like process can be stabilized by the heat removal via the heat conductivity and the heat exchange with the thermal bath. This problem is less important in metallic systems. If one deals with substances which conduct heat very well, the temperature may be treated as a constant and so no kinetic equation additional to one for the order parameter is necessary. But for materials which do not conduct heat so well, we may need a second equation to determine the temperature distribution. Therefore the interphase boundary motion can be determined by the rate of heat transfer in the system. In the recent review (12) our theory of the kink motion of the interphase boundary (14,16,17) has been examined. The necessity of taking into account processes of dissipati(;n of energy released (or additionaly absorbed) during the time of transition has been analysed (12). The electric-field driven kinetics of ferroelectric interphase boundaries have not been studied up to now. In this paper we obtain a criterion of necessity of considering the heat transfer effect on the interphase boundary propagation. We show here that at first-order phase transitions in ferroelectrics-semiconductors the thermal conductivity is not a controlling process and

Condensation of Nitrogen: Implications for Pluto and Triton

We have observed in the laboratory that nitrogen condenses initially as a transparent layer if the deposition rate is less than about 3 μm/hr. To correlate our laboratory results with the Voyager observations of Triton and ground-based observations of Pluto, we have calculated the nitrogen deposition rates on these bodies. The maximum deposition rate for Pluto (with 40K icy surface temperature) is calculated to be about 1.65 μm/hr and for Triton is ≈1.38 μm/hr at 38 K. This implies that nitrogen on these bodies may preferentially condense as a transparent layer. Voyager 2 observations in August 1989 revealed that Triton's northern hemisphere had an overall lower albedo than the southern hemisphere. This was surprising since at that time deposition of fresh N2frost should have taken place over most of Triton's northern hemisphere (subsolar point was 45°S). In contrast, the subliming southern cap was seen as a bright feature. Our new approach to this problem is based on the combination of the energy balance calculations and the laboratory results. We explain the darker northern hemisphere by the condensation of an initially transparent layer on a dark substrate, which might be dark organics produced by UV photolysis of CH4ice. The bright southern cap can be a result of N2shattering due to the earlier passage of the cubic–hexagonal phase transition fronts. If there is a similar puzzling north/south albedo asymmetry on Pluto, as indicated by two independent sets of observations (M. W. Buie, D. J. Tholen, and K. Horne, 1992,Icarus97, 211–227; E. F. Young and R. P. Binzel, 1993,Icarus102, 134–149), our results offer an explanation for it. We also infer an original grain size of N2ice on Triton and, possibly, on Pluto. The role of impurities is discussed.

Driving Force on Phase Transition Fronts in Thermoelectroelastic Crystals

Starting from known physical balance laws and constitutive equations, this work develops in a rational number the canonical balance laws of momentum and energy at both regular and singular material points. This is achieved in the framework of the quasi-electrostatics of thermoelectroelastic crystals, with a view to providing a sound basis for the study of electroelastic fracture, and of the propagation of phase transition fronts. The latter receive special attention with the formulation of a true thermomechanics in which it is shown that a hot surface heat source develops at thermodynamically irreversible points of progress of such fronts. The expression of the driving force acting on such fronts in these conditions is obtained in terms of the relevant Hugoniot-Gibbs functional. This provides the basis for the formulation of simple criteria of progress of the front.